1. State the problem: Find $\sqrt[3]{64}$. 2. Use the cube root rule: $\sqrt[3]{a}=b$ means $b^3=a$. 3. Write $64$ as a perfect cube: $64=4^3$. 4. Substitute into the rule: $$\sqrt[3]{64}=\sqrt[3]{4^3}=4.$$ 5. Check: $4^3=64$, so the answer is correct. Final answer: $\sqrt[3]{64}=4$.